This reminds me of a bug I found in an internal tool. We only had about 200 users, but somehow Apache would run out of workers because they were all busy serving some kind of request. Turns out our Apache configuration was wrong specifically in the case of serving the favicon. If you requested the favicon, it would get in a redirect loop, increasing the length of the url a little more each time until it hit the maximum url length and gave up. A new job like this would get kicked off every time any user visited a page, and it'd take several minutes before it finally gave up. So every user was unwittingly opening tons of long-running requests, with no indication that they were doing anything.
Yeah, I hit something sort of similar but on the client side: While clicking around a single-page webapp, Chrome would manage to use up all its outbound connections (10 or so) trying to download non-existent favicons, leaving none for real use. And those favicon requests somehow never timed out. Chrome's favicon handling is pretty bad.
